We prove that for any knot K, there exists a one-vertex triangulation of the 3-sphere containing an edge forming K. The proof is constructive, and based on fully augmented links. We use our method to produce “complicated” simplicial triangulations of the 3-sphere that we show are smallest possible, up to a constant multiplicative factor.
Introduction A substantial proportion of e-bike injuries and fatalities occur in motor-vehicle lanes, where riders are exposed to mixed traffic and higher crash risk, potentially offsetting the health benefits of e-bike use. Notably, many riders still enter motor-vehicle lanes even when dedicated bicycle lanes are available. Such lane intrusion increases exposure to hazardous interactions with vehicles and diminishes the safety benefits of cycling infrastructure. Therefore, identifying psychological factors associated with lane intrusion is important for informing injury-prevention interventions. Methodology An online survey of 729 e-bike riders (650 valid for analysis) assessed self-reported e-bike lane intrusion behaviour (e-bike LIB) using a newly developed Riding Lane Intrusion Behaviour Questionnaire, and assessed infrastructure perception, perceived safety, perceived risk, and Theory of Planned Behaviour constructs. We combined multi-group structural equation modelling with explainable machine learning to examine theory-informed associations among infrastructure perception, key psychological constructs, and e-bike LIB, and to explore potential non-linear patterns. Results Attitude, perceived behavioural control, and subjective norms were positively associated with self-reported lane intrusion, with attitude showing the strongest association. Infrastructure perception was negatively associated with self-reported lane intrusion and exhibited a possible non-linear pattern, with larger marginal reductions at higher levels of infrastructure perception. As infrastructure perception increased from low levels, perceived safety increased while perceived risk decreased, and these perceptions were further associated with e-bike LIB primarily indirectly through attitude and perceived behavioural control. Conclusions E-bike LIB should be understood as a preventable mixed-traffic exposure rather than a neutral lane-choice decision. The findings suggest that infrastructure provision should be complemented by behavioural measures targeting favourable attitudes, overconfidence, and permissive social norms. In poorer riding environments, stricter enforcement and improvements to the perceived usability and visibility of existing facilities may help discourage non-compliance with available bicycle lanes.
Objectives Out-of-pocket (OOP) costs and financial toxicity remain significant barriers to equitable cancer care globally. This review systematically identifies and compares survey-based approaches used to measure patient- and household-level OOP expenditures and financial burden across diverse cancer settings. Methods A systematic search (2021-2025) of PubMed, Embase, and EBSCO databases identified studies that used survey methodologies, including patient-reported outcome measure instruments to estimate OOP spending and financial toxicity among cancer patients. Two reviewers independently screened studies and extracted data on key methodological characteristics including instrument type, cost domains, recall periods, validation practices, and reporting conventions to compare measurement approaches across studies. Results Based on the eligibility criteria, 45 studies were included. Survey tools showed substantial heterogeneity in structure, terminology, and measurement practices. Studies differed widely in the cost domains captured (direct medical, direct nonmedical, and indirect costs) and used recall periods ranging from a few days to 156 months. Reporting of currency, cost year, and conversion methods was inconsistent. Most relied on bespoke, nonvalidated questionnaires to measure objective financial burden, whereas validated patient-reported outcome measures, such as the Comprehensive Score for Financial Toxicity (COST) measures, were used inconsistently for subjective financial distress. This methodological variation substantially limited comparability across studies and hindered synthesis of patient-level financial burden. Conclusions Survey-based methods for measuring OOP costs and financial burden in cancer care remain highly variable. Establishing minimum methodological and reporting standards for core cost domains, recall periods, and financial burden indicators may improve comparability of evidence while allowing context-specific adaptation across health systems.
The rapid growth and subsequent utilization of distributed energy resources (DERs), particularly in low-voltage networks, is pushing distribution networks to the brink of their hosting capacity. Distribution network operators, especially in DER-rich countries such as Australia, are exploring novel technologies and effective strategies to enhance DER integration while maintaining network integrity, as an alternative to costly network upgrades. One such technology developed and introduced is the network exchanger (NEx), which aims to enhance hosting capacity by regulating voltage, mitigating current imbalance, and power factor correction at the distribution transformer. This paper presents a comprehensive evaluation of NEx, compared with on-load tap changers and distribution static synchronous compensators, through an extensive simulation study that models projected growth in photovoltaic and electric vehicle penetration as per the Integrated System Plan released by the Australian Energy Market Operator, using a large-scale, real-world distribution network comprising over 8000 buses, and located in Queensland, Australia. Simulation results indicate breaches in network integrity under business-as-usual conditions in both step-change and progressive-change scenarios. The performance of each technology is benchmarked across six low-voltage networks that exhibit higher levels of network violations and photovoltaic curtailment, with NEx resolving all voltage breaches and reducing transformer loading and photovoltaic curtailment by noticeable amounts, which can aid in delaying costly network augmentation.
The Monash-Peradeniya-Kodikara (MPK) framework interprets the volumetric behaviour of compacted unsaturated soils in the void ratio − moisture ratio − net stress (e-ew-p) space without requiring suction as an independent constitutive variable. Nevertheless, explicit knowledge of suction distributions within this volumetric space can provide additional insight into hydromechanical behaviour and facilitate comparison with conventional suction-based frameworks. This paper reconstructs continuous suction surfaces on and inside the Loading Wetting State Boundary Surface (LWSBS) within the MPK space by combining suction topology inferred from published experimental datasets with a constrained mathematical reconstruction methodology consistent with MPK principles. The reconstruction is divided into three regions relative to the Line of Optimums (LOO). At the wet side of the LOO, suction contours on the LWSBS are reconstructed using effective stress relationships and semilogarithmic compression relationships. At the dry side of the LOO, suction contours are reconstructed from Soil Water Characteristic Curves (SWCCs) extended towards the dry condition using cubic Bézier curves. Suction contours inside the LWSBS are reconstructed on constant net stress planes using fifth-order Bézier curves to generate smooth, continuous, and nonintersecting suction surfaces. Application to kaolin and Merri Creek soils produces suction profiles consistent with reported experimental trends, including suction reduction during constant moisture loading and a distinct transition in contour curvature across the LOO. The reconstructed suction surfaces preserve the fundamental structure of the MPK framework while providing the first explicit continuous hydraulic representation of suction within the MPK volumetric state space. They enable estimation of suction at intermediate soil states where direct measurements are unavailable, facilitate comparison with conventional suction-based interpretations, and establish a foundation for future constitutive, numerical, and coupled hydromechanical modelling within the MPK framework.
